DE 100 60 490 A1 describes a device for monitoring a vehicle electrical system, and which includes a sensor for measuring electrical current flowing in a connecting line. In order to cover an overall larger measurement range than can be recorded using an individual sensor for the purpose of measuring the current, two sensors with different measurement ranges are provided. A Hall sensor is provided for measuring currents between 10 mA and 10 A. A resistor (shunt) which is arranged in the connecting line is provided as a sensor for measuring currents between 1 A and 10 kA. The voltage drop caused by the current to be measured at the shunt is used as an auxiliary measurement variable for determining the value of the current to be measured.